If equals :

Engineering

Mathematics

Properties of Definite Integral

Question

If $g (x) = \int_{0}^{x} \cos 4 t dt, then g (x + π)$ equals :

g(x) – g(π)

$\frac{g (x)}{g (π)}$

g(x).g(π)

(g(x))^g(π)

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Given $g (x) = \int_{0}^{x} \cos 4 t dt$

Now, $g (x + π) = \int_{0}^{x + π} \cos 4 t dt = \int_{0}^{π} \cos 4 t dt + \int_{π}^{x + π} \cos 4 t dt$

$= \int_{0}^{π} \cos 4 t dt + \int_{0}^{x} \cos 4 t dt = g (π) + g (x)$

⇒ g(x + π) = g(x) + g(π)

but g(π) = 0

$∴ g (x + π) = g (x) + g (π) = g (x) - g (π)$